Related papers: Statistical reduced order modelling for the parame…
This paper presents an information-theoretic approach for model reduction for finite time simulation. Although system models are typically used for simulation over a finite time, most of the metrics (and pseudo-metrics) used for model…
In this paper, we present an adaptive framework for constructing a pseudo-optimal reduced model for the frequency-limited H2-optimal model order reduction problem. We show that the frequency-limited pseudo-optimal reduced-order model has an…
We propose a stochastic model reduction strategy for deterministic and stochastic slow-fast systems with finite time-scale separation. The stochastic model reduction relaxes the assumption of infinite time-scale separation of classical…
In this paper, we propose a randomized generalized multiscale finite element method (Randomized GMsFEM) for flow problems with parameterized inputs and high-contrast heterogeneous media. The method employs a data-driven predictor to…
In frequency-limited model order reduction, the objective is to maintain the frequency response of the original system within a specified frequency range in the reduced-order model. In this paper, a mathematical expression for the…
High temperatures and structural deformations can compromise the functionality and reliability of new components for mechatronic systems. Therefore, high-fidelity simulations (HFS) are employed during the design process, as they enable a…
We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell…
In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…
In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…
Waveform inversion seeks to estimate an inaccessible heterogeneous medium from data gathered by sensors that emit probing signals and measure the generated waves. It is an inverse problem for a second order wave equation or a first order…
A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
Reduced-order plasma models that can efficiently predict plasma behavior across various settings and configurations are highly sought after yet elusive. The demand for such models has surged in the past decade due to their potential to…
Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
Parametric reduced-order modelling often serves as a surrogate method for hemodynamics simulations to improve the computational efficiency in many-query scenarios or to perform real-time simulations. However, the snapshots of the method…
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…
The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…